Canonical connection on a class of Riemannian almost product manifolds

TL;DR

This paper studies the canonical connection on a specific class of Riemannian almost product manifolds with non-integrable structures, providing construction and characterization through a Lie group example.

Contribution

It introduces a detailed analysis of the canonical connection on non-integrable Riemannian almost product manifolds and constructs an explicit example using a Lie group.

Findings

Characterization of the canonical connection in the non-integrable case

Explicit example constructed via a Lie group

Insights into the geometric structure of such manifolds

Abstract

The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an example by a Lie group.